the science of summing resolution (question)

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hello,

I'd like get a true numerical understanding of resolution when a bunch
of tracks get summed to a 2-track mix.

If you have a 32bit float digital engine going down to 24 bit at the
stereo fader, how does this stack up against something like an SSL
9000j analog?

Analog could appear "unlimited", but I believe the analog mix bus has
to step things down to get all the tracks balanced in the stereo fader,
and then you come up against the s/n ratio and maximum dynamic range
that an analog circuit can provide.

I would think the 32bit/24bit digital signal flow described above would
match or outperform even a very fine analog stereo mix bus in terms of
dynamic range, resolution and s/n ratio.

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<genericaudioperson@hotmail.com> wrote in message
news:1108704146.346166.181210@o13g2000cwo.googlegroups.com
> hello,
>
> I'd like get a true numerical understanding of resolution when a bunch
> of tracks get summed to a 2-track mix.
>
> If you have a 32bit float digital engine going down to 24 bit at the
> stereo fader, how does this stack up against something like an SSL
> 9000j analog?

Done right, 32 bit digital kills analog, accuracy-wise.

> Analog could appear "unlimited",

In some alternative universe where there is no such thing as thermal and
other electrical noise, perhaps.

> but I believe the analog mix bus has
> to step things down to get all the tracks balanced in the stereo
> fader, and then you come up against the s/n ratio and maximum dynamic
> range that an analog circuit can provide.

Thus, analog is not unlimited.

> I would think the 32bit/24bit digital signal flow described above
> would match or outperform even a very fine analog stereo mix bus in
> terms of dynamic range, resolution and s/n ratio.

It's all the same, or maybe Clyde Shannon really was the bozo that some
audiophiles would like to make him out to be. ;-)

BTW, you forgot frequency response.

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On Fri, 18 Feb 2005 07:20:47 -0800, Jay Kadis <jay@ccrma.stanford.edu>
wrote:

>In article <O4Wdnau0XuWPTYjfRVn-iQ@comcast.com>,
> "Arny Krueger" <arnyk@hotpop.com> wrote:
>
>[snip]
>>
>> It's all the same, or maybe Clyde Shannon really was the bozo that some
>> audiophiles would like to make him out to be. ;-)
>>
>
>Clyde may have been a bozo: Claude Shannon however, knew about sampling theory.

You mean those audiophools have been ragging on the wrong guy all
this time?

>-Jay

-----
http://mindspring.com/~benbradley

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<genericaudioperson@hotmail.com> wrote:
>
>as an abstract idea. how many theoretical decibels is 32 bits or 24
>bits? it's really hard for an analog circuit to get above 116db of
>true performance. i'm somehow thinking 32/24 would have a theoretical
>value higher than that.

6 dB/bit.

So a 16-bit system gives you 96 dB. A 24-bit system would give you
144 dB, if the converters were that good, which they aren't. A 32-bit
fixed-point system would give you 192 dB range, which is nearly as wide as
the range of theoretically possible sounds at sea level.

By going to floating point you can go even wider. But converter noise
floors and monotonicity are what kill you anyway.
--scott
--
"C'est un Nagra. C'est suisse, et tres, tres precis."

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<genericaudioperson@hotmail.com> wrote in message
news:1108742921.308623.103610@z14g2000cwz.googlegroups.com

> yeah, a lot of other things could be looked at, frequency response,

That's important.

> linearity,

That's the identical same thing as dynamic range in digital systems.

>slew rates.

That relates to linearity and frequency response. Modern digital systems do
have finite and relatively low slew rates, but they lack slew rate limiting
since they lack nonlinear distortion.

> over time i've become much more of an "accuracy freak" rather than a
> "warmth and character" person. it's not that i don't like sounds that
> have character. it's just that i would like to start with maximum
> resolution and transparency first, and then make decisions from there.

Agreed. I have no problems with EFX, but I like to have the opportunity to
second guess myself, and third guess myself, and...

> also, i've actually grown to dislike knobs and big things. i like the
> screen better, and i'm much better at troubleshooting a computer than
> an analog circuit.. so it looks like i'm best off getting the signal
> into the computer with top-quality a-d, and then staying 32/24 for the
> duration.

That's pretty much what I do. I wish the irreducable analog parts of my
system were as good as the digital ones.

> as an abstract idea. how many theoretical decibels is 32 bits or 24
> bits?

It's roughly six times the number of bits plus about 2. For 32 bits that is
about 194 dB, while for 24 bits that is 146 dB.

>it's really hard for an analog circuit to get above 116db of true
>performance.

That is the equivalent of about 19 bits.

>i'm somehow thinking 32/24 would have a theoretical value higher than
>that.

You're right, and it is all good. However, it is so much more than the real
world analog domain including acoustics, that's its about meaningless.

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Arny Krueger wrote:

> Done right, 32 bit digital kills analog, accuracy-wise.

I'm still wondering about what happens when the FPU normalizes a 32-bit
float: normally truncation of less-significant bits occurs, but how is
dither applied during the loss of precision?

No one seems to talk about this, as if the mantissa in a float is
somehow preserved in all its 24-bit glory, when actually, the result of
each and every calculation likely requires a truncation. What are the
sonic effects of this? Are there any?

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"Scott Dorsey" <kludge@panix.com> wrote in message
news:cv58oo$9ti$1@panix2.panix.com
> Arny Krueger <arnyk@hotpop.com> wrote:
>> <genericaudioperson@hotmail.com> wrote in message
>>
>>> linearity,
>>
>> That's the identical same thing as dynamic range in digital systems.

> No. That's dynamic range PLUS monotonicity. Monotonicity is a big
> deal.

Monotonicity? That hasn't been much of an issue since sigma-delta converters
took over the audio market. They are essentially guaranteed to be linear and
monotonic by design.

> And note that SOME of the more modern systems may be monotonic at some
> frequencies, but not at others. This is a bad thing.

I've seen linearity problems at high frequencies, but those converters were
simply nonlinear, not lacking in monotonicity.

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On Fri, 18 Feb 2005 16:40:09 -0500, "Arny Krueger" <arnyk@hotpop.com>
wrote:

>Monotonicity? That hasn't been much of an issue since sigma-delta converters
>took over the audio market. They are essentially guaranteed to be linear and
>monotonic by design.

Theoretically. But adherence to theory depends critically on
perfect summing junctions on the output end and perfect
slewing to the next sample on the input end. Real world
limitations here effect monotonicity in weird signal-
dependent ways.

Chris Hornbeck
"Loved him; hated her." -Danny Kaye on the Himalaya's

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"S O'Neill" <nopsam@nospam.net> wrote in message
news:ap-dnez5X-rot4vfRVn-3Q@omsoft.com
> Arny Krueger wrote:
>
>> Done right, 32 bit digital kills analog, accuracy-wise.
>
> I'm still wondering about what happens when the FPU normalizes a
> 32-bit float: normally truncation of less-significant bits occurs,
> but how is dither applied during the loss of precision?
>
> No one seems to talk about this, as if the mantissa in a float is
> somehow preserved in all its 24-bit glory, when actually, the result
> of each and every calculation likely requires a truncation. What are
> the sonic effects of this? Are there any?

Letsay that we provide 1 LSB worth of dither. Dynamic range drops from 146
dB to at very worst 140 dB. Real world analog still can't touch it.

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"Tommi M." <tomppaaREMOvE@kolumbus.fi> wrote in message
news:cv7131$nrn$1@phys-news1.kolumbus.fi
> "Scott Dorsey" <kludge@panix.com> wrote in message
> news:cv54ib$lnt$1@panix2.panix.com...
>> A 32-bit
>> fixed-point system would give you 192 dB range, which is nearly as
>> wide as the range of theoretically possible sounds at sea level.
>
> Are you referring to the maximum negative pressure (0 psi)?

Sounds about right.

> Btw, is there any limit to the positive pressure change?

Compress air enough and it turns into something like plasma. I don't think
that Shure, EV, Neumann or Schoeps have a lot of plasma mics in their online
catalogs. Recording performances made with a plasma bass guitar could be
hazardous to your health. Check with your friendly neighborhood Sandia Labs
distributor.

Archived from groups: rec.audio.pro (More info?)

My heavily modified Soundcraft Delta uses a balanced discrete/opamp
summing design. It measures -95 db stereo crosstalk 20 to 20k hz.
Distortion measures .0004% THD+noise. CCIF IMD measures .00015%. Noise
levels in this stage measures minus 134 db referenced to +4.

It also has punch, balls, spatialness, depth and width, all things
missing from a digital sum. Oh, it gets cleaner with reduced levels,
while digital gets worse. With high end analog stuff like this
available I believe only those with limited budgets or a lack of
concern with quality would lead those to find a digital mix solution
over an analog one of this quality.

It's not that expensive to go this route, after all, I only paid $750
for the console used.

Jim Williams
Audio Upgrades

Jim Williams
Audio Upgrades

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"Arny Krueger" <arnyk@hotpop.com> wrote in message
newso2dnZN1v9zTG4rfRVn-1A@comcast.com...
> <jwilliams3@audioupgrades.com> wrote in message
> news:1108833704.455934.5440@z14g2000cwz.googlegroups.com
> > My heavily modified Soundcraft Delta uses a balanced discrete/opamp
> > summing design. It measures -95 db stereo crosstalk 20 to 20k hz.
> > Distortion measures .0004% THD+noise. CCIF IMD measures .00015%. Noise
> > levels in this stage measures minus 134 db referenced to +4.
>
> Really nice analog performance. Seems like a good front end for a LynxTWO.
>
> > It also has punch, balls, spatialness, depth and width, all things
> > missing from a digital sum. Oh, it gets cleaner with reduced levels,
> > while digital gets worse.
>
> It would really help my respect for analog bigots if they weren't so prone
> to gratuitous posts of techno-trash-talk like this.


It's an experience and resulting opinion, different from yours. You're
talking about respect, but your choice of words doesn't even show tolerance
towards opinions that differ from yours.

Having been particularly interested in the subject of analog vs. digital
summing for a long time and after extensive tests and comparisons between
multiple analog and digital setups, I completely agree with Jim Williams
(Note to self: snatch the first Delta that shows up for sale). When it comes
to terms like "punch, balls, spatialness, depth and width", for me there's
no contest, even in case of lesser analog mixers.

However, all those people out there who prefer digital summing can't be
wrong. Many of them prove their case
with great mixes, perhaps not superior in the above mentioned categories,
but still great overall. So the most derogatory conclusion that I've been
able to come up with is that we don't hear and appreciate things the same
way. There's no right or wrong here.

Predrag

Archived from groups: rec.audio.pro (More info?)

"Predrag Trpkov" <predrag.trpkovNeSpamu@ri.htnet.hr> wrote in message
news:cv8ghh$fv5$1@ls219.htnet.hr
> "Arny Krueger" <arnyk@hotpop.com> wrote in message
> newso2dnZN1v9zTG4rfRVn-1A@comcast.com...
>> <jwilliams3@audioupgrades.com> wrote in message
>> news:1108833704.455934.5440@z14g2000cwz.googlegroups.com
>>> My heavily modified Soundcraft Delta uses a balanced discrete/opamp
>>> summing design. It measures -95 db stereo crosstalk 20 to 20k hz.
>>> Distortion measures .0004% THD+noise. CCIF IMD measures .00015%.
>>> Noise levels in this stage measures minus 134 db referenced to +4.
>>
>> Really nice analog performance. Seems like a good front end for a
>> LynxTWO.
>>
>>> It also has punch, balls, spatialness, depth and width, all things
>>> missing from a digital sum. Oh, it gets cleaner with reduced levels,
>>> while digital gets worse.
>>
>> It would really help my respect for analog bigots if they weren't so
>> prone to gratuitous posts of techno-trash-talk like this.

> It's an experience and resulting opinion, different from yours.

No, its just trash talk. Digital done even halfways right is as free of
nonlinear distoriton at low levels as high levels. It's not fair to
criticize digital because it doesn't have increasing nonlinear distortion at
high levels.


>You're talking about respect, but your choice of words doesn't even show
> tolerance towards opinions that differ from yours.

That digital done even halfways right has no increase in nonlinear
distoriton at low levels is a simple, well-known, easily-demonstrable
scientific fact.

> Having been particularly interested in the subject of analog vs.
> digital summing for a long time and after extensive tests and
> comparisons between multiple analog and digital setups, I completely
> agree with Jim Williams (Note to self: snatch the first Delta that
> shows up for sale). When it comes to terms like "punch, balls,
> spatialness, depth and width", for me there's no contest, even in
> case of lesser analog mixers.

Why not tell us about the details of your tests?

> However, all those people out there who prefer digital summing can't
> be wrong.

All those millions of people who thought Corvairs were safe couldn't have
been wrong either. All those people who think that McDonalds make the best
hamburgers can't be wrong.

> Many of them prove their case
> with great mixes, perhaps not superior in the above mentioned
> categories, but still great overall.

Mixing is largely an art. Once equipment reaches certain reasonable levels
of performance, the quality of the mix is in the experience, ears and
hand/eye coordination of the mixer. If someone does great mixes, all it
shows about his equipment is that he's avoided the poorer equipment out
there.

> So the most derogatory
> conclusion that I've been able to come up with is that we don't hear
> and appreciate things the same way. There's no right or wrong here.

There is the slight matter of scientific fact versus old wife's tales.

Archived from groups: rec.audio.pro (More info?)

"Arny Krueger" <arnyk@hotpop.com> wrote in message
news:RpCdnQmd0YxNGoXfRVn-2g@comcast.com...
> "Predrag Trpkov" <predrag.trpkovNeSpamu@ri.htnet.hr> wrote in message
> news:cv8ghh$fv5$1@ls219.htnet.hr
> > "Arny Krueger" <arnyk@hotpop.com> wrote in message
> > newso2dnZN1v9zTG4rfRVn-1A@comcast.com...
> >> <jwilliams3@audioupgrades.com> wrote in message
> >> news:1108833704.455934.5440@z14g2000cwz.googlegroups.com
> >>> My heavily modified Soundcraft Delta uses a balanced discrete/opamp
> >>> summing design. It measures -95 db stereo crosstalk 20 to 20k hz.
> >>> Distortion measures .0004% THD+noise. CCIF IMD measures .00015%.
> >>> Noise levels in this stage measures minus 134 db referenced to +4.
> >>
> >> Really nice analog performance. Seems like a good front end for a
> >> LynxTWO.
> >>
> >>> It also has punch, balls, spatialness, depth and width, all things
> >>> missing from a digital sum. Oh, it gets cleaner with reduced levels,
> >>> while digital gets worse.
> >>
> >> It would really help my respect for analog bigots if they weren't so
> >> prone to gratuitous posts of techno-trash-talk like this.
>
> > It's an experience and resulting opinion, different from yours.
>
> No, its just trash talk. Digital done even halfways right is as free of
> nonlinear distoriton at low levels as high levels. It's not fair to
> criticize digital because it doesn't have increasing nonlinear distortion
at
> high levels.


Everything's perfect in the ideal world. Even digital audio. In such a world
you probably wouldn't feel the urge to insult people just because you happen
to disagree with a single statement, taken out of the context.


> >You're talking about respect, but your choice of words doesn't even show
> > tolerance towards opinions that differ from yours.
>
> That digital done even halfways right has no increase in nonlinear
> distoriton at low levels is a simple, well-known, easily-demonstrable
> scientific fact.
>
> > Having been particularly interested in the subject of analog vs.
> > digital summing for a long time and after extensive tests and
> > comparisons between multiple analog and digital setups, I completely
> > agree with Jim Williams (Note to self: snatch the first Delta that
> > shows up for sale). When it comes to terms like "punch, balls,
> > spatialness, depth and width", for me there's no contest, even in
> > case of lesser analog mixers.
>
> Why not tell us about the details of your tests?


Oh sure, you've really motivated me.



> > However, all those people out there who prefer digital summing can't
> > be wrong.
>
> All those millions of people who thought Corvairs were safe couldn't have
> been wrong either. All those people who think that McDonalds make the best
> hamburgers can't be wrong.


I was talking about preferences, not about beliefs, scientific facts or
life-threatening misconceptions. There's no right or wrong when it comes to
preferences in audio.



> > Many of them prove their case
> > with great mixes, perhaps not superior in the above mentioned
> > categories, but still great overall.
>
> Mixing is largely an art. Once equipment reaches certain reasonable levels
> of performance, the quality of the mix is in the experience, ears and
> hand/eye coordination of the mixer. If someone does great mixes, all it
> shows about his equipment is that he's avoided the poorer equipment out
> there.
>
> > So the most derogatory
> > conclusion that I've been able to come up with is that we don't hear
> > and appreciate things the same way. There's no right or wrong here.
>
> There is the slight matter of scientific fact versus old wife's tales.


Scientific facts are subject to scrutiny, revisions, changes... unlike the
necessity to maintain a civilized debate.

Predrag

Archived from groups: rec.audio.pro (More info?)

"Predrag Trpkov" <predrag.trpkovNeSpamu@ri.htnet.hr> wrote in message
news:cvapv0$o36$1@ls219.htnet.hr
> "Arny Krueger" <arnyk@hotpop.com> wrote in message
> news:RpCdnQmd0YxNGoXfRVn-2g@comcast.com...

>> Digital done even halfways right is as
>> free of nonlinear distoriton at low levels as high levels. It's not
>> fair to criticize digital because it doesn't have increasing
>> nonlinear distortion at high levels.

> Everything's perfect in the ideal world. Even digital audio. In such
> a world you probably wouldn't feel the urge to insult people just
> because you happen to disagree with a single statement, taken out of
> the context.

It's not an insult to call errors wrong.

In the digital domain practice approaches theory far mo-better than it does
in the analog domain. In the digital domain having 1,000 dB dynamic range is
possible with off-the-shelf software, even fairly inexpensive stuff. Please
get back when you find a piece of analog gear with even 200 dB dynamic
range.

>> Why not tell us about the details of your tests?

> Oh sure, you've really motivated me.

Run away from your claims, if you wish. Don't let the door...

>>> However, all those people out there who prefer digital summing can't
>>> be wrong.
>>
>> All those millions of people who thought Corvairs were safe couldn't
>> have been wrong either. All those people who think that McDonalds
>> make the best hamburgers can't be wrong.

> I was talking about preferences, not about beliefs,

Horsefeathers. You made a specific claim about digital having increasing
distortion at low levels.

>scientific facts
> or life-threatening misconceptions. There's no right or wrong when it
> comes to preferences in audio.

Then talk about preferencs and leave the bad science out of it.

>>> Many of them prove their case
>>> with great mixes, perhaps not superior in the above mentioned
>>> categories, but still great overall.
>>
>> Mixing is largely an art. Once equipment reaches certain reasonable
>> levels of performance, the quality of the mix is in the experience,
>> ears and hand/eye coordination of the mixer. If someone does great
>> mixes, all it shows about his equipment is that he's avoided the
>> poorer equipment out there.
>>
>>> So the most derogatory
>>> conclusion that I've been able to come up with is that we don't hear
>>> and appreciate things the same way. There's no right or wrong here.

>> There is the slight matter of scientific fact versus old wife's
>> tales.

> Scientific facts are subject to scrutiny, revisions, changes...

So here's a common gambit. Make false claims and when they blow up in your
face, try to pass them off as preferences.

Archived from groups: rec.audio.pro (More info?)

jwilliams3@audioupgrades.com wrote:

> Test results are fine, but savy designers know that test gear will only
> tell you if something is wrong, only the ears will tell you if
> something is right.

Jim, that would be a great signature, or plaque on the wall, or
something. Excellent!